Przemyslaw Prusinkiewicz
Resume of achievements in research
Summary. Przemyslaw Prusinkiewicz has pioneered the use of computational models in
developmental plant biology. He has advanced the methods for plant modeling and
visualization based on the theory of L-systems, designed programming languages for
specifying the models, and led the implementation of widely used software for simulating
plant development. In interdisciplinary collaborations with biologists, he has constructed
models that elucidate several key aspects of plant development, including phyllotactic and
branching patterns. The models relate molecular mechanisms to macroscopic forms and
unify distinct developmental processes and structures. Prusinkiewicz’s results have also
advanced the state of the art in image synthesis.
Background and early results. Seminal advancement in plant modeling is due to theoretical
biologist Aristid Lindenmayer, who in 1968 proposed the formalism of L-systems to
describe the development of filamentous and branching multicellular organisms. In spite of
extensive theoretical studies of L-systems in the 1970s, however, their relevance to
biological problems was uncertain. In 1986, Prusinkiewicz defined a geometric
interpretation of L-systems, which drastically enhanced the ability to visualize L-systems
models [130]. On this basis, he and his student Jim Hanan created an L-system-based plant
simulation program, which they used in collaboration with Lindenmayer to model
herbaceous plants. This work demonstrated conclusively the power of L-systems to
simulate and visualize developmental processes controlled by diverse regulatory
mechanisms [121]. The models also showed that the apparently complex structures and
developmental patterns of plants may emerge from strikingly simple rules and mechanisms.
The book, The Algorithmic Beauty of Plants [55], co-authored by Prusinkiewicz and
Lindenmayer, extended these early results. It reached a wide audience of computer
scientists, plant biologists and the general public, popularizing plant modeling as a research
field. It is considered “the first comprehensive volume on the computer simulation of plant
development” (Wikipedia) and continues to be widely known and cited (over 2000 citations
to date). Realistic computer-generated images created for this book advanced the state of
the art in realistic image synthesis. The paper [130] and the book [55] also revealed a
surprising link between L-systems and fractals. In related work, Prusinkiewicz introduced
L-systems as a tool for automatic generation of music and geometric patterns found in
Indian folk art. These results positioned L-systems as a mathematical object of broad
interdisciplinary interest.
Advances in modeling methodology and software. Throughout the 1990s, Prusinkiewicz’s
research was focused on extending the modeling power of L-systems, addressing the needs
of both biological modeling and image synthesis. Parametric L-systems [55] formalized
the notion of quantitative attributes associated with plant components. These attributes
have made it possible to simulate nuanced geometrical details of modeled structures, e.g.,
the arrangement of plant organs into spiral phyllotactic patterns, and the self-similar
structure of fern leaves. Further nuancing was made possible by incorporating the concept
of positional information into L-systems [88]. Parametric L-systems also opened the door
for the modeling of plants according to measured architectural data, simulation of
regulatory processes at the physiological [23] and genetic (e.g. [25,18,15]) levels, and
modeling of plant biomechanics. Differential L-systems [104] provided the basis for
simulating and animating development in continuous time, as opposed to the sequence of
discrete stages stipulated by the original definition of L-systems. Environmentallysensitive and open L-systems introduced a framework for simulating the interaction of
plants with their environment, including plant responses to pruning and competition of
plants for space, light and water [99]. In recent work, Prusinkiewicz and his students used
open L-systems to explain the development and diversity of trees as a result of their selforganization [6]. Further extensions have made it possible to model entire plant
communities and ecosystems with L-systems [84]. Dr. Prusinkiewicz’s contributions to the
modeling and visualization of biological structures were recognized with the ACM
SIGGRAPH 1997 Achievement Award, one of the highest awards in the field of Computer
Graphics (he was the first recipient of this award working outside the U.S.), and the 2009
Achievement Award from the Canadian Human Computer Communications Society.
To specify models, Prusinkiewicz and his students designed and implemented two
programming languages: cpfg, well suited for constructing simple models, and L+C,
advantageous when constructing comprehensive models [29]. These languages and the
software incorporating them are used for plant modeling worldwide.
Prusinkiewicz and his student David Fracchia also introduced a physically-based
interpretation of map L-systems, introduced in 1979 by Lindenmayer and Grzegorz
Rozenberg to extend L-systems from branching structures to cell layers. This interpretation
pioneered the concept of defining the shape and size of cells as an equilibrium between
osmotic pressure and wall tension [55]. Subsequently, Prusinkiewicz and his student Colin
Smith introduced the formalism of vertex-vertex systems [81], which is more expressive
and convenient to use than map L-systems. The modeling software based on vertex-vertex
systems has been applied to construct many recently published models of plant
morphogenesis, e.g. [18,8,1]. Further development of this software is now being carried
out in collaboration with Pierre Barbier de Reuille and Richard Smith at the University of
Bern, Switzerland.
Applications of models to the studies of development. In the last decade, Prusinkiewicz has
championed the use of computational models as a tool for understanding the link between
molecular-level mechanisms and the macroscopic form of plants. He has carried out this
research in collaboration with some of the leading developmental plant biologists,
promoting modeling as a tool for interpreting experimental data. Prusinkiewicz’s
collaboration with Enrico Coen (John Innes Centre) has contributed to the establishment of
this technique [25]. Their specific results include a model explaining the development,
diversity, and potential evolutionary paths of inflorescences [15]. The model showed that
inflorescences of different types can be generated by the same simple mechanism, given
different values of two parameters under genetic control. It also predicted an association
between inflorescence architecture and climate, and explained why some evolutionary
transitions between closely related plant taxa were rare. A more recent model explained
cell division patterns leading to the formation of stomata in leaves [1]. In addition to
addressing one of the classical patterning problems in plants, the model extended the
Errera rule, a fundamental geometric rule governing cell division, from symmetric to
asymmetric divisions.
The dominant theme of Prusinkiewicz’s research on the molecular basis of plant
development has been the role of the plant growth regulator auxin. According to the
canalization hypothesis proposed in the late 1960s by Tsvi Sachs and first implemented
computationally in 1980 by Graeme Mitchison, auxin plays a unique morphogenetic role
due to its ability to control its own transport between cells. Prusinkiewicz and his
postdoctoral fellow Anne-Gaëlle Rolland-Lagan showed that the canalization hypothesis
was generally consistent with new molecular data [20]. They also observed that the
canalization model tended to create the shortest connections between auxin sources and
sinks. This result led to a geometric model of leaf pattern formation in leaves [22], which is
the most faithful model of vein pattern formation to date. In subsequent research involving
canalization, Prusinkiewicz worked with Ottoline Leyser (University of York, now
Cambridge) to explain the regulation of bud activation. They have shown that the
feedback between auxin transport and the polarization of its transporters, inherent in
canalization, suffices to explain the bud activation patterns observed in wild type and
manipulated Arabidopsis plants [5]. This result provides a key insight into the branching
architecture of Arabidopsis and other plants.
In collaboration with Cris Kuhlemeier and his team (University of Bern), Prusinkiewicz
and his student Richard Smith have also created a model of phyllotaxis, the arrangement of
plant organs on their supporting axes [18]. The conspicuous geometric regularity of
phyllotactic patterns has attracted the interest of biologists, mathematicians, physicists and
chemists for almost 200 years. The simulation model, along with a concurrently published
model developed at Caltech, is considered “a first attempt to bridge the gap between the
long history of models for phyllotaxis and molecular biology” (M. Heisler and H. Jönsson,
Current Opinion in Plant Biology 10 (2007): 92-97). More recently, Prusinkiewicz and
Miltos Tsiantis (University of Oxford) designed a related model to explain the
development of leaf serration [3]. It is the first computational model explaining an aspect
of leaf form in molecular terms. Different modes of auxin transport polarization underlying
the canalization hypothesis and assumed in the models of phyllotaxis and leaf growth were
reconciled in [8] by assuming that both modes may operate concurrently.
Conclusion. By integrating ideas from biology and computer science, Prusinkiewicz has
advanced the theoretical foundations and practical methods of plant modeling. In
collaboration with biologists, he has championed the use of modeling in developmental
plant biology and elucidated several fundamental mechanisms of plant development. These
results improve our understanding of mechanisms producing diverse developmental
patterns and forms of plants.